Mental Maths

Mental Maths helps in strengthening your ‘number sense’. One becomes more aware of how numbers ‘play’ – an important aspect to be learned because maths is something that builds on itself. Students who are not so flexible in splitting and combining the numbers in easier ways, not only get baffled executing the standard algorithms in their heads but often yield incorrect results, without any clue of its inaccuracy.

Mental Maths strategies relieves the students of the computational part of mathematics, thus enabling them to focus towards the bigger mathematical idea under consideration.

Besides, Mental Maths also helps in developing the confidence of students and it is also an excellent way to stimulate your brain. I start my session daily with a 10-minute Mental Math activity. Following three problems were posed to them, one after the other, to solve mentally.

Problem-1
How much is 9.8 x 2.5 ?

Kanchan says,
I will consider the numbers as 98 and 25. Further, lets round up 98 as 100. So now, 25 times 100 gives 2500. But I have taken 2 times 25 more..
So, 98 x 25 = 2500 – 50 = 2450
Now, since I had multiplied each of the two given numbers by 10, the obtained product will be 100 times more than the desired one. Hence the actual answer will be 2450 / 100 = 24.5

Student-2: I considered 12.5 as 125. Now, 125 x 8 = 1000. Then, 125 x 0.5 means half of 125 = 62.5…. So we get 1062.5….. Now we divide this answer by 10 as we have worked with 125 instead of 12.5 …. This gives 106.25

Student-3:
14 x 40 = 560
14 x 50 = 700
Since 644 is between 560 and 700… So, answer is going to be between 40 and 50

Now, 644 ends in 4.. So if 14 x some number ends in 4, then that some number should end in 1 or 4… But 560 + 14 cannot be equal to 644… So 560 + 14 x 6 will give 644…. So answer is 40 + 6 = 46
1) How would you solve these 3 problems mentally?
2) How about your students/ children?
3) What are your views about the approaches used by these students?
4) What are your views about the language used by them to communicate their reasoning?

Waiting for your responses…
How can students be guided towards discovery by asking the right questions, so that they are able to discover and correct mistakes on their own? Some answers may be found in the various stories and Maths conversations recorded in my blog.